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Two contradictory derivations of Killing equation

As an overall comment, I stress that conservation of $Q$ is valid for the Killing vector $\xi$ if the considered curve is a geodesic. Let us come to the issue. First of all, generally speaking, the ...
Valter Moretti's user avatar
2 votes

Two contradictory derivations of Killing equation

Both approaches are fine. In the first approach, the analysis is done at the coordinate/component level of the equations. Simply asking the question how does $Q$ very with $\tau$ if we write ...
TimRias's user avatar
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1 vote

Two contradictory derivations of Killing equation

I think the problem lies in the notation. I guess Tong is treating the components $\xi_\mu$ as scalars for which we have $\frac{\mathrm{d}}{\mathrm{d}\tau}=u^\alpha\partial_\alpha$. And the ...
Silas's user avatar
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1 vote
Accepted

Doubt on conservation of angular momentum for Kepler's laws

The definition of a plane can be written as $\vec{a}\cdot \vec{r} = 0$, where $\vec{a}$ is any vector perpendicular to the plane. In this case, you have a vector quantity $\vec{L}$, which is from its ...
ProfRob's user avatar
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1 vote

Doubt on conservation of angular momentum for Kepler's laws

The angular momentum ${\bf L}$ of a point-like particle is proportional to the vector product of position ${\bf r}$ and velocity ${\bf v}$. It is a vector orthogonal to the plane containing ${\bf r}$ ...
GiorgioP-DoomsdayClockIsAt-90's user avatar
2 votes
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Which kinds of systems are described by a heat equation?

So you’ve asked for other examples where the “heat equation” comes up. This is really a diffusion equation in general. The first thing worth mentioning is, your derivation is making a particular ...
CR Drost's user avatar
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-1 votes

Which kinds of systems are described by a heat equation?

The following is intended to expand on hyportnex's comment in one particular direction; you may or may not find it useful. Your path from the conservation equation of an extensive quantity $X$ (I'll ...
Chemomechanics's user avatar
-1 votes
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Is there any phenomenon where opposite reaction (Newton's 3rd Law) is not fulfilled?

While Newton's Third Law of Motion is a fundamental principle in physics, there are some situations where it may appear to be violated or where the reaction force is not immediately apparent. However, ...
Ansh Tandon's user avatar
0 votes

Is there any phenomenon where opposite reaction (Newton's 3rd Law) is not fulfilled?

All forces occur in pairs. There are no isolated forces. See; http://hyperphysics.phy-astr.gsu.edu/hbase/Newt.html As stated in the link, there are no known exceptions. Hope this helps
Bob D's user avatar
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6 votes

Noether's theorem by a taste of logic

Noether’s theorem is a mathematical theorem. It connects conservation laws to the properties of Lagrangian functionals. If these properties are contradicted by experiment then this means that a ...
my2cts's user avatar
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3 votes

Designing a thought experiment on Noether's Theorem

Experiments on crystals are translationally variant because the crystal structure is only the same up to translations that reproduce the same structure, in such cases there is "crystal momentum&...
mike1994's user avatar
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5 votes

Have all the symmetries of the standard model of particle physics been found?

My answer is also ‘No’ but by direct construction: over the past few years, various research groups have understood new symmetries of the Standard Model. Over the past decade, field theorists have ...
SethK's user avatar
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1 vote

How do you solve instantaneous 3 body collisions

How did you solve it for 2 particles? I ask because there's not actually enough information in the question to determine what happens in a collision. Consider a simple example of two equal mass ...
Cort Ammon's user avatar
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1 vote

Do bodies stick together after an inelastic oblique collision?

The case you are referring to is where the objects are like in this drawing: where the surface of interaction (the red lines) is slippery and the objects are malleable enough to absorb all velocity ...
Jos Bergervoet's user avatar
5 votes

Energy of moving Sine-Gordon breather

Since the sine-Gordon theory is $SO(1,1)$ invariant, if you can find the energy for the stationary breather, you can find it for a moving breather as well. All that is required is a Lorentz boost; ...
Buzz's user avatar
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-1 votes

Charge conservation in ohmic material - Apparent paradox

As I understand it, the questioner's claim is that the equation $\frac{\partial Q}{\partial t}+\frac{\sigma}{\epsilon_0}Q=0$ is derived only from the standard Maxwell equations. As a result, $Q$ is ...
HEMMI's user avatar
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0 votes

Could we deduce energy, momentum and angular momentum conservation laws from only Galilean relativity?

No. Galilean invariance is about "how systems stay physically equivalent under galilean transformations" and Noether's theorem is about "what things stay the same along a dynamical ...
Lourenco Entrudo's user avatar
4 votes
Accepted

Charge conservation in ohmic material - Apparent paradox

Differential problems are defined in a domain and require boundary conditions, and the solution to be "regular enough" for the differential equations to hold. If you're dealing with a body ...
basics's user avatar
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0 votes

Do bodies stick together after an inelastic oblique collision?

Some of this might be vocabulary. In the usual head on inelastic collision, the bodies wind up at the same velocity in contact. Typically they deform, turning kinetic energy into heat. I would say ...
mmesser314's user avatar
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2 votes

Do bodies stick together after an inelastic oblique collision?

Do bodies stick together after an inelastic oblique collision? If the collision is perfectly inelastic, yes. If coefficient of restitution is zero it should mean that after collision the relative ...
Bob D's user avatar
  • 73.6k
0 votes

Why do people say that Hamilton's principle is all of classical mechanics? How to get Newton's third law?

Newton's classical mechanics and Hamiltonian mechanics are not covering the same possibilities for the system to be described. And Lagrangian mechanics describes only the union of the two sets, this [...
Jos Bergervoet's user avatar

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